Optimization on the real symplectic group
نویسندگان
چکیده
منابع مشابه
Least-Squares on the Real Symplectic Group
The present paper discusses the problem of least-squares over the real symplectic group of matrices Sp(2n,R). The least-squares problem may be extended from flat spaces to curved spaces by the notion of geodesic distance. The resulting non-linear minimization problem on manifold may be tackled by means of a gradient-descent algorithm tailored to the geometry of the space at hand. In turn, gradi...
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we examine the symplectic group $sp_{2m}(q)$ and its correspondingaffine subgroup. we construct the affine subgroup and show that itis a split extension. as an illustration of the above we study theaffine subgroup $2^5{:}sp_4(2)$ of the group $sp_6(2)$.
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We define a family of groups that include the mapping class group of a genus g surface with one boundary component and the integral symplectic group Sp.2g;Z/ . We then prove that these groups are finitely generated. These groups, which we call mapping class groups over graphs, are indexed over labeled simplicial graphs with 2g vertices. The mapping class group over the graph is defined to be ...
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In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called the Toledo invariant. This invariant is bounded by a Milnor–Wood type inequality. Our main result is a count of the number of connected components of the mod...
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Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic zero. We have a left (G×G)-action on G defined as (g1, g2) ·x := g1xg −1 2 . A (G×G)-equivariant embedding G ↪→ X is said to be regular (cf. [BDP], [Br, §1.4]) if the following conditions are satisfied: (i) X is smooth and the complement X \G is a normal crossing divisor D1 ∪ · · · ∪Dn. (ii) Ea...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2020
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-020-01369-9